Thèse de doctorat en Mathématiques appliquées
Soutenue en 2005
Méthodes variationelles pour des modèles fonction-structure de plantes : identification de paramètre, contrôle et assimilation de données
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The thesis is devoted to a unified variational approach for diverse applications, such as parameter calibration, optimal control and data assimilation, based on plant architecture and functioning. The mathematical formulation of the functional-structural plant model GreenLab is completed by the introduction of an empirical formula on environmental factors to mimic photosynthesis. A soil water balance submodel has been integrated into GreenLab to descript the dynamic soil-plant system. The dynamics formulation enables efficient numerical solutions for the variational systems by introducing the corresponding adjoint model. Differentiation algorithms are employed to derive adjoint code by hand in a systematic way directly from GreenLab source code. This variational approach is followed to solve an optimal control problem of sunflower water supply for better fruit production. Data assimilation concept is introduced to decrease the model uncertainties both in initial conditions and external model parameters. The defined problems and optimal control techniques proposed in this thesis reveal possible agronomic applications